Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and systems and, more particularly, to mechanisms and techniques for reconstructing wave-fields (e.g., deghosting, redatuming, denoising, interpolating, etc.) based on seismic data collected with receivers located either on streamers or on or close to the ocean bottom.
Discussion of the Background
Marine seismic data acquisition and processing generate a profile (image) of the geophysical structure (subsurface) under the seafloor. While this profile does not provide an accurate location for oil and gas, it suggests, to those trained in the field, the presence or absence of oil and/or gas. Thus, providing a high-resolution image of the subsurface is an ongoing process for the exploration of natural resources, including, among others, oil and/or gas.
During a seismic gathering process, as shown in FIG. 1, a vessel 110 tows plural detectors 112, which are disposed along a cable 114. Cable 114 together with its corresponding detectors 112 are sometimes referred to, by those skilled in the art, as a streamer 116. Vessel 110 may tow plural streamers 116 at the same time. Streamers may be disposed horizontally, i.e., lie at a constant depth z1 relative to the ocean surface 118. Also, plural streamers 116 may form a constant angle (i.e., the streamers may be slanted) with respect to the ocean surface as disclosed in U.S. Pat. No. 4,992,992, the entire content of which is incorporated herein by reference.
Still with reference to FIG. 1, vessel 110 may also tow a seismic source 120 configured to generate an acoustic wave 122a. Acoustic wave 122a propagates downward and penetrates the seafloor 124, eventually being reflected by a reflecting structure 126 (reflector R). Reflected acoustic wave 122b propagates upward and is detected by detector 112. For simplicity, FIG. 1 shows only two paths 122a corresponding to the acoustic wave. Parts of reflected acoustic wave 122b (primary) are recorded by various detectors 112 (recorded signals are called traces) while parts of reflected wave 122c pass detectors 112 and arrive at the water surface 118. Since the interface between the water and air is well approximated as a quasi-perfect reflector (i.e., the water surface acts as a mirror for acoustic waves), reflected wave 122c is reflected back toward detector 112 as shown by wave 122d in FIG. 1. Wave 122d is normally referred to as a ghost wave because it is due to a spurious reflection. Ghosts are also recorded by detector 112, but with a reverse polarity and a time lag relative to primary wave 122b if the detector is a hydrophone. The degenerative effect that ghost arrival has on seismic bandwidth and resolution is known. In essence, interference between primary and ghost arrivals causes notches, or gaps, in the frequency content recorded by detectors.
Recorded traces may be used to determine the subsurface (i.e., earth structure below surface 124) and to determine the position and presence of reflectors 126. However, ghosts disturb the accuracy of the final image of the subsurface and, for at least this reason, various methods exist for removing ghosts, i.e., deghosting, from the acquired seismic data. These methods were designed for deghosting seismic data recorded with horizontal or slanted streamers.
The above-discussed methods are not appropriate for seismic data collected with new streamer configurations, e.g., having a curved profile as illustrated in FIG. 2. Deghosting methods for streamers having a curved profile have recently been developed, mainly by the assignee of this application, as later discussed. Such a configuration has a streamer 252 with a curved profile. The curved profile may have any shape. One example of a curved profile is defined by three parametric quantities, z0, s0 and hc. Note that not the entire streamer has to have the curved profile. The first parameter z0 indicates the depth of the first detector 254a relative to the water's surface 258. Second parameter s0 is related to the slope of the initial part of streamer 252 relative to a horizontal line 264. The example shown in FIG. 2 has initial slope s0 equal to substantially 3 percent. Other values may be used. Note that the streamer 252 profile in FIG. 2 is not drawn to scale because a slope of 3 percent is relatively slight. Third parameter hc indicates a horizontal length (distance along the X axis in FIG. 2 measured from first detector 254a) of the streamer's curved portion. This parameter may be in the range of hundreds to thousands of meters.
For such streamers, a deghosting process has been disclosed, for example, in U.S. Pat. No. 8,456,951 (herein '951) authored by R Soubaras, the entire content of which is incorporated herein. According to the '951 patent, a method for deghosting uses joint deconvolution for migration and mirror migration images to generate a final image of a subsurface. Deghosting is performed at the end of processing (during an imaging phase) and not at the beginning, as with traditional methods. Further, the '951 patent discloses that no datuming step is performed on the data.
Another method that addresses variable-depth data is disclosed by U.S. patent application Ser. No. 13/334,776 (herein '776) authored by G. Poole. This method uses a surface datum tau-p model that represents input shot data. A transform from the tau-p model to a shot domain (offset-time) combines the operations of redatuming and reghosting. The use of variable-depth streamer data combined with reghosting ensures that a single point in the tau-p domain satisfies a range of different ghost lags, therefore, making use of variable-depth data notch diversity, which ensures effective receiver deghosting.
FIG. 3 illustrates how one point 302 in the tau-p domain 320 reverse transforms to a pair of lines 304 and 306 in time-space domain 310, at actual streamer position and mirror streamer datum, respectively. The energy relating to mirror cable datum has reverse polarity (−1) compared to the cable datum (+1) as also illustrated in FIG. 3. Note that the time-space (or time-offset) domain 310 has time t on the vertical axis, and offset h between the receiver recording the wave and the source generating the wave, along the X axis, while tau-p domain 320 has the tau coordinate (intercept in the time-space domain) along the Y axis, and the p coordinate (slope in the time-space domain) along the X axis. Application '776 uses a least squares formulation given by:d=Lp  (1)or, in the expanded matrix form,
                                          (                                                                                d                    1                                                                                                                    d                    2                                                                                                                    d                    N                                                                        )                    =                                    (                                                                                                                  ⅇ                                                                              -                            2                                                    ⁢                          π                          ⁢                                                                                                          ⁢                          if                          ⁢                                                                                                          ⁢                                                      τ                            pr                                                                                              -                                              ⅇ                                                                              -                            2                                                    ⁢                          π                          ⁢                                                                                                          ⁢                          if                          ⁢                                                                                                          ⁢                                                      τ                            gh                                                                                                                                                                                                                                                                                                                                                                                                                              )                        ⁢                          (                                                                                          p                      1                                                                                                                                  p                      2                                                                                                                                  p                      3                                                                                                                                  p                      M                                                                                  )                                      ,                            (        2        )            where column vector d contains a frequency slice from the shot domain data (known), column vector p contains the surface datum tau-p model (unknown), and matrix L makes the transform (known) from the surface tau-p model to the input shot data. Matrix L combines the operations of redatuming and reghosting.
The time shifts for primary (up-going) and ghost (down-going) wave fields are given by:τpr=(hn+Δh)sm−Δτ  (3)τgh=(hn−Δh)sm+Δτ,  (4)where hn is the offset of a given trace in column vector d, sm is the slowness of a given trace in the surface tau-p model, Δh is the offset perturbation as described in the '776 application, and Δτ is the temporal perturbation as also described in the '776 application. Equation (1) can be solved in the time or spectral (e.g., frequency) domain using linear inversion. The method can be applied on the whole shot (cable-by-cable) or in spatial windows of a user-defined number of channels.
However, existing methods relate to pressure measurements made, for example, by hydrophones. Currently, the new streamer generation is capable of measuring not only pressure but also particle motion data, e.g., displacement, velocity, differential pressure, acceleration, etc. Thus, there is a need to process not only pressure measurements, but also particle motion data. Accordingly, it would be desirable to provide systems and methods with such capabilities.